Quantum-classical correspondence of a system of interacting bosons in a triple-well potential

E. R. Castro1,2, Jorge Chávez-Carlos3, I. Roditi2, Lea F. Santos4, and Jorge G. Hirsch5

1Instituto de Física da UFRGS Av. Bento Gonçalves 9500, Porto Alegre, RS, Brazil
2Centro Brasileiro de Pesquisas Físicas/MCTI, 22290-180, Rio de Janeiro, RJ, Brazil
3Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Cuernavaca, Morelos 62210, México
4Department of Physics, Yeshiva University, New York, New York 10016, USA
5Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apdo. Postal 70-543, C.P. 04510 Cd. Mx., México

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We study the quantum-classical correspondence of an experimentally accessible system of interacting bosons in a tilted triple-well potential. With the semiclassical analysis, we get a better understanding of the different phases of the quantum system and how they could be used for quantum information science. In the integrable limits, our analysis of the stationary points of the semiclassical Hamiltonian reveals critical points associated with second-order quantum phase transitions. In the nonintegrable domain, the system exhibits crossovers. Depending on the parameters and quantities, the quantum-classical correspondence holds for very few bosons. In some parameter regions, the ground state is robust (highly sensitive) to changes in the interaction strength (tilt amplitude), which may be of use for quantum information protocols (quantum sensing).

Studies of the quantum-classical correspondence provide insights into the properties of both the quantum system and its classical counterpart. In this work, we explore the quantum-classical correspondence to locate the quantum phase transition points of an experimentally accessible system of interacting bosons in a triple-well potential. With the semiclassical analysis, we get a better understanding of the different phases of the quantum system and how they could be used for quantum information science.

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Cited by

[1] Karin Wittmann W., E. R. Castro, Angela Foerster, and Lea F. Santos, "Interacting bosons in a triple well: Preface of many-body quantum chaos", Physical Review E 105 3, 034204 (2022).

[2] Gary McCormack, Rejish Nath, and Weibin Li, "Hyperchaos in a Bose-Hubbard Chain with Rydberg-Dressed Interactions", Photonics 8 12, 554 (2021).

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